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Further Results on Transcendental Meromorphic Solutions of some Certain Types of Nonlinear Differential Equations
Jian Jun ZHANG
Acta Mathematica Sinica, Chinese Series ›› 2018, Vol. 61 ›› Issue (4) : 529-540.
PDF(458 KB)
PDF(458 KB)
Further Results on Transcendental Meromorphic Solutions of some Certain Types of Nonlinear Differential Equations
We shall deal with the existence and the form of transcendental meromorphic solutions of nonlinear differential equation of the form fn+Qd(z, f)=p1(z)eα1(z)+ p2(z)eα2(z), where n ≥ 4 is an integer, Qd(z, f) is a differential polynomial in f of degree d ≤ n-3 with rational functions as its coefficients, p1, p2 are non-vanishing rational functions and α1, α2 are nonconstant polynomials. By utilizing Nevanlinna value distribution theory, we can derive conditions concerning the terms p1, p2, α1 and α2 that are necessary for the existence and the form of a transcendental meromorphic solution of the equation. In particular, we also consider the existence and the form of transcendental meromorphic solution of the equation when Qd(z, f)=a(z)ff' with n=4, where a(z) is a non-vanishing rational function.
Nevanlinna theory / differential equations / meromorphic solutions / zeros / poles {{custom_keyword}} /
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